Which of the following numbers is a multiple of 10? ${61,75,85,100,103}$
Solution: The multiples of $10$ are $10$ $20$ $30$ $40$ ..... In general, any number that leaves no remainder when divided by $10$ is considered a multiple of $10$ We can start by dividing each of our answer choices by $10$ $61 \div 10 = 6\text{ R }1$ $75 \div 10 = 7\text{ R }5$ $85 \div 10 = 8\text{ R }5$ $100 \div 10 = 10$ $103 \div 10 = 10\text{ R }3$ The only answer choice that leaves no remainder after the division is $100$ $ 10$ $10$ $100$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $10$ are contained within the prime factors of $100$ $100 = 2\times2\times5\times5 10 = 2\times5$ Therefore the only multiple of $10$ out of our choices is $100$. We can say that $100$ is divisible by $10$.